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Re: MX2 2015 Integration Marathon no, at pi/2, you still get finite, actually zero ( by multiplying cos^n both numerator and denominator )

Re: MX2 2015 Integration Marathon yes thats same as i did

Re: MX2 2015 Integration Marathon substitute x=\tan\theta , then carry out IBP twice. i got I=\frac{n}{n^2-1}

Re: HSC 2015 3U Marathon well, as Carrotsticks said, any finite number of terms may not uniquely determine a pattern. but the formula T_n=\frac{7n^2-5n}{20(2^n-1)} definitely gives one of the possible patterns

Re: HSC 2015 3U Marathon only listing three terms, a pattern may not be clearly defined. like the denominators: 10, 30, 70, ... the next one could be 70+60=130, could also be 70+80=150, could even be something else

Re: MX2 2015 Integration Marathon substitution x=\sin^2\theta

Re: HSC 2015 4U Marathon new question $ Prove that $ P(x)=x^5-ax+1=0 $ has three distinct real roots if and only if $ a>5\left(\frac{1}{2}\right)^{8/5}.

Re: MX2 2015 Integration Marathon good start, but you do not need to actually integrate it, you just need an estimation, why not try to apply the comparison property of definite integrals

Re: MX2 2015 Integration Marathon just to fix the latex problem \int \frac{1+x}{\sqrt{1-x^{2}}} dx \\ =\frac{-1}{2} \int {\frac{-2}{\sqrt{1-x^{2}}} + \frac{-2x}{\sqrt{1-x^{2}}} \\ ={\frac{-1}{2}} (-2sin^{-1}(x) + 2 \sqrt{1-x^{2}}) is this what you wanted ?

is the starting position 2i-8j+k or 2i+8j+k ?

Re: MX2 2015 Integration Marathon what is dx then ?

binomial probabilities ?

lol lots of fun

Re: MX2 2015 Integration Marathon \int_{0}^{100\pi} \sqrt{cos^{2}(x) + sin^{2}(x) - cos^{2}(x) + sin^{2}(x)} dx=\int_{0}^{100\pi} \sqrt{{2}} \sqrt{sin^{2}(x)} dx=\int_{0}^{100\pi} \sqrt{{2}} |sin(x)|dx $ Now, the graph of $ |sin(x)| $ will repeat every pi/2 interval as it is a reflection...

Re: HSC 2015 4U Marathon - Advanced Level i got \frac{19}{36} for part (i) and \frac{3}{7} for part (ii). i am not sure this is true or not, because i didn't use those facts.

Re: urgent area between curve however if the same integral is asked after the differentiation, that is within the syllabus of 3U.

Re: urgent area between curve 2u or 3u don't do this one, probably you meant \frac{4x}{e^{x^2}} ?

not the simple addition, should be the linear combination, how about try 2b-3c+a ?

Re: HSC 2015 4U Marathon lol. so it is -1 at the end but not +1, I was thinking if it was +1, there is no solution in that form.

no